Showing
119
question(s) for
UK Class 10
—
Subject:
Mathematics
Mathematics
Q1.
Solve the quadratic equation x² - 5x + 6 = 0.
Answer:
Factorising gives (x - 2)(x - 3) = 0. Therefore x = 2 or x = 3.
Mathematics
Q2.
What is the quadratic formula?
Answer:
For an equation ax² + bx + c = 0, the solutions are x = (-b ± √(b² - 4ac)) / 2a.
Mathematics
Q3.
What is a prime number?
Answer:
A prime number is a whole number greater than 1 that has exactly two factors: 1 and itself.
Mathematics
Q4.
What is the difference between a factor and a multiple?
Answer:
A factor divides a number exactly, while a multiple is obtained by multiplying a number by an integer.
Mathematics
Q5.
What is the highest common factor (HCF)?
Answer:
The HCF is the greatest positive integer that divides two or more numbers exactly.
Mathematics
Q6.
What is the lowest common multiple (LCM)?
Answer:
The LCM is the smallest positive integer that is a multiple of two or more numbers.
Mathematics
Q7.
What is a rational number?
Answer:
A rational number is a number that can be written as a fraction p/q, where p and q are integers and q is not zero.
Mathematics
Q8.
What is an irrational number?
Answer:
An irrational number cannot be expressed exactly as a fraction of two integers and has a non-terminating, non-repeating decimal expansion.
Mathematics
Q9.
What is standard form?
Answer:
Standard form writes a number as A × 10^n, where 1 ≤ A < 10 and n is an integer.
Mathematics
Q10.
How do you convert a percentage into a decimal?
Answer:
Divide the percentage by 100. For example, 35% becomes 0.35.
Mathematics
Q11.
How do you find a percentage of an amount?
Answer:
Convert the percentage to a decimal and multiply it by the amount.
Mathematics
Q12.
What is percentage change?
Answer:
Percentage change is calculated as change divided by the original value, multiplied by 100.
Mathematics
Q13.
What is a percentage increase?
Answer:
A percentage increase measures how much a quantity has risen relative to its original value.
Mathematics
Q14.
What is a percentage decrease?
Answer:
A percentage decrease measures how much a quantity has fallen relative to its original value.
Mathematics
Q15.
What is a ratio?
Answer:
A ratio compares two or more quantities of the same type using division.
Mathematics
Q16.
How can a ratio be simplified?
Answer:
Divide every part of the ratio by their greatest common factor.
Mathematics
Q17.
What is direct proportion?
Answer:
Two quantities are directly proportional when one is a constant multiple of the other, so their ratio remains constant.
Mathematics
Q18.
What is inverse proportion?
Answer:
Two quantities are inversely proportional when their product remains constant as one quantity increases and the other decreases.
Mathematics
Q19.
What is a recurring decimal?
Answer:
A recurring decimal is a decimal in which one or more digits repeat indefinitely.
Mathematics
Q20.
What is an index?
Answer:
An index, or exponent, indicates how many times a number or algebraic expression is multiplied by itself.
Mathematics
Q21.
What is the zero index rule?
Answer:
For any non-zero number a, a^0 = 1.
Mathematics
Q22.
What is the rule for multiplying powers with the same base?
Answer:
When multiplying powers with the same base, add their indices: a^m × a^n = a^(m+n).
Mathematics
Q23.
What is the rule for dividing powers with the same base?
Answer:
When dividing powers with the same base, subtract the indices: a^m ÷ a^n = a^(m-n).
Mathematics
Q24.
What does a negative index mean?
Answer:
A negative index represents the reciprocal of the corresponding positive power: a^-n = 1/a^n.
Mathematics
Q25.
What is a surd?
Answer:
A surd is an irrational root that cannot be simplified to a rational number.
Mathematics
Q26.
What is the difference between an expression and an equation?
Answer:
An expression represents a mathematical quantity, while an equation states that two expressions are equal.
Mathematics
Q27.
What is algebraic simplification?
Answer:
Algebraic simplification means rewriting an expression in an equivalent but simpler form by collecting like terms and applying algebraic rules.
Mathematics
Q28.
What are like terms?
Answer:
Like terms have exactly the same variables raised to the same powers and can therefore be combined.
Mathematics
Q29.
What is the distributive law?
Answer:
The distributive law states that a(b + c) = ab + ac.
Mathematics
Q30.
What does it mean to expand brackets?
Answer:
Expanding brackets means multiplying the terms outside or inside the brackets and removing the brackets using the distributive law.
Mathematics
Q31.
What does it mean to factorise an expression?
Answer:
Factorising means writing an algebraic expression as a product of simpler factors.
Mathematics
Q32.
What is a linear equation?
Answer:
A linear equation is an equation in which the highest power of the variable is one.
Mathematics
Q33.
What is a quadratic equation?
Answer:
A quadratic equation is an equation that can be written in the form ax² + bx + c = 0, where a is not zero.
Mathematics
Q34.
What is the quadratic formula?
Answer:
For ax² + bx + c = 0, the solutions are x = (-b ± √(b² - 4ac)) / 2a.
Mathematics
Q35.
What is the discriminant of a quadratic equation?
Answer:
The discriminant is b² - 4ac. It determines the number and type of solutions of a quadratic equation.
Mathematics
Q36.
What does the discriminant tell us when it is positive?
Answer:
A positive discriminant gives two distinct real solutions.
Mathematics
Q37.
What does the discriminant tell us when it is zero?
Answer:
A zero discriminant gives one repeated real solution.
Mathematics
Q38.
What does the discriminant tell us when it is negative?
Answer:
A negative discriminant means there are no real solutions.
Mathematics
Q39.
What is completing the square?
Answer:
Completing the square is a method of rewriting a quadratic expression in the form a(x - h)² + k.
Mathematics
Q40.
What is a simultaneous equation?
Answer:
A simultaneous equation is part of a system of equations that must be solved together to find common values of the variables.
Mathematics
Q41.
What is a sequence?
Answer:
A sequence is an ordered list of numbers that follows a particular rule or pattern.
Mathematics
Q42.
What is an arithmetic sequence?
Answer:
An arithmetic sequence is a sequence in which the difference between consecutive terms is constant.
Mathematics
Q43.
What is the nth term of an arithmetic sequence?
Answer:
The nth term is given by a + (n - 1)d, where a is the first term and d is the common difference.
Mathematics
Q44.
What is a geometric sequence?
Answer:
A geometric sequence is a sequence in which each term is obtained by multiplying the previous term by a constant ratio.
Mathematics
Q45.
What is a function?
Answer:
A function is a rule that assigns exactly one output to each permitted input.
Mathematics
Q46.
What is function notation?
Answer:
Function notation represents a function using a symbol such as f(x), where x is the input.
Mathematics
Q47.
What is the gradient of a straight line?
Answer:
The gradient measures the steepness of a line and is calculated as change in y divided by change in x.
Mathematics
Q48.
What is the equation of a straight line?
Answer:
A common form is y = mx + c, where m is the gradient and c is the y-intercept.
Mathematics
Q49.
What is the y-intercept?
Answer:
The y-intercept is the point where a graph crosses the y-axis.
Mathematics
Q50.
What is the gradient of a horizontal line?
Answer:
The gradient of a horizontal line is zero.
Mathematics
Q51.
What is the gradient of a vertical line?
Answer:
A vertical line has an undefined gradient because its change in x is zero.
Mathematics
Q52.
What is the equation of a circle centred at the origin?
Answer:
The equation is x² + y² = r², where r is the radius.
Mathematics
Q53.
What is Pythagoras' theorem?
Answer:
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
Mathematics
Q54.
What is the hypotenuse?
Answer:
The hypotenuse is the longest side of a right-angled triangle and is opposite the right angle.
Mathematics
Q55.
What is trigonometry?
Answer:
Trigonometry is the study of relationships between angles and sides of triangles.
Mathematics
Q56.
What does SOH stand for?
Answer:
SOH represents sine = opposite ÷ hypotenuse.
Mathematics
Q57.
What does CAH stand for?
Answer:
CAH represents cosine = adjacent ÷ hypotenuse.
Mathematics
Q58.
What does TOA stand for?
Answer:
TOA represents tangent = opposite ÷ adjacent.
Mathematics
Q59.
What is the sine rule?
Answer:
The sine rule states that a/sin A = b/sin B = c/sin C for a triangle.
Mathematics
Q60.
What is the cosine rule?
Answer:
The cosine rule states that a² = b² + c² - 2bc cos A.
Mathematics
Q61.
What is the area of a triangle?
Answer:
The area of a triangle is 1/2 × base × perpendicular height.
Mathematics
Q62.
What is the area of a circle?
Answer:
The area of a circle is πr², where r is the radius.
Mathematics
Q63.
What is the circumference of a circle?
Answer:
The circumference is 2πr, where r is the radius.
Mathematics
Q64.
What is the volume of a prism?
Answer:
The volume of a prism is the area of its cross-section multiplied by its length.
Mathematics
Q65.
What is the volume of a cylinder?
Answer:
The volume of a cylinder is πr²h, where r is the radius and h is the height.
Mathematics
Q66.
What is the volume of a sphere?
Answer:
The volume of a sphere is 4/3πr³.
Mathematics
Q67.
What is the surface area of a sphere?
Answer:
The surface area of a sphere is 4πr².
Mathematics
Q68.
What is the volume of a cone?
Answer:
The volume of a cone is 1/3πr²h.
Mathematics
Q69.
What is an angle at a point?
Answer:
Angles at a point add up to 360 degrees.
Mathematics
Q70.
What is the sum of angles in a triangle?
Answer:
The interior angles of a triangle add up to 180 degrees.
Mathematics
Q71.
What is the sum of the interior angles of a quadrilateral?
Answer:
The interior angles of a quadrilateral add up to 360 degrees.
Mathematics
Q72.
What are corresponding angles?
Answer:
Corresponding angles are angles in matching positions when a transversal crosses two lines.
Mathematics
Q73.
What are alternate angles?
Answer:
Alternate angles lie on opposite sides of a transversal between two lines and are equal when the lines are parallel.
Mathematics
Q74.
What are co-interior angles?
Answer:
Co-interior angles lie on the same side of a transversal between two parallel lines and add up to 180 degrees.
Mathematics
Q75.
What is similarity in geometry?
Answer:
Similar shapes have the same shape, corresponding angles equal and corresponding sides in the same ratio.
Mathematics
Q76.
What is congruence?
Answer:
Congruent shapes have exactly the same size and shape, although they may have different orientations.
Mathematics
Q77.
What is a vector?
Answer:
A vector has both magnitude and direction and can be represented by a directed line segment.
Mathematics
Q78.
What is a scalar quantity?
Answer:
A scalar quantity has magnitude but no direction, such as mass, time or temperature.
Mathematics
Q79.
How are vectors added?
Answer:
Vectors are added by combining their corresponding components or by placing them head-to-tail geometrically.
Mathematics
Q80.
What is a translation?
Answer:
A translation moves every point of a shape by the same distance in the same direction.
Mathematics
Q81.
What is a reflection?
Answer:
A reflection produces a mirror image of a shape across a specified mirror line.
Mathematics
Q82.
What is a rotation?
Answer:
A rotation turns a shape about a fixed centre through a specified angle and direction.
Mathematics
Q83.
What is an enlargement?
Answer:
An enlargement changes the size of a shape using a scale factor while maintaining its shape.
Mathematics
Q84.
What is probability?
Answer:
Probability measures how likely an event is to occur and has values from 0 to 1.
Mathematics
Q85.
What is the probability of an impossible event?
Answer:
The probability of an impossible event is 0.
Mathematics
Q86.
What is the probability of a certain event?
Answer:
The probability of a certain event is 1.
Mathematics
Q87.
What is the complement of an event?
Answer:
The complement is the event that the original event does not occur, and P(not A) = 1 - P(A).
Mathematics
Q88.
What is an independent event?
Answer:
Two events are independent if the occurrence of one does not affect the probability of the other.
Mathematics
Q89.
What is conditional probability?
Answer:
Conditional probability is the probability of an event occurring given that another event has already occurred.
Mathematics
Q90.
What is a sample space?
Answer:
A sample space is the set of all possible outcomes of a probability experiment.
Mathematics
Q91.
What is the mean?
Answer:
The mean is calculated by adding all the values and dividing the total by the number of values.
Mathematics
Q92.
What is the median?
Answer:
The median is the middle value when a data set is arranged in order.
Mathematics
Q93.
What is the mode?
Answer:
The mode is the value that occurs most frequently in a data set.
Mathematics
Q94.
What is the range?
Answer:
The range is the difference between the largest and smallest values in a data set.
Mathematics
Q95.
What is an outlier?
Answer:
An outlier is a value that is unusually far from the other values in a data set.
Mathematics
Q96.
What is a frequency table?
Answer:
A frequency table organises data by showing each value or class and how often it occurs.
Mathematics
Q97.
What is grouped data?
Answer:
Grouped data is numerical data organised into intervals or classes rather than listing every individual value.
Mathematics
Q98.
What is a histogram?
Answer:
A histogram displays continuous grouped data using adjoining bars, with frequency represented according to class width.
Mathematics
Q99.
What is frequency density?
Answer:
Frequency density is calculated as frequency divided by class width.
Mathematics
Q100.
What is cumulative frequency?
Answer:
Cumulative frequency is the running total of frequencies up to a particular value or class boundary.
Mathematics
Q101.
What is a scatter graph?
Answer:
A scatter graph displays pairs of numerical values to investigate the relationship between two variables.
Mathematics
Q102.
What is correlation?
Answer:
Correlation describes the strength and direction of a relationship between two variables.
Mathematics
Q103.
What is positive correlation?
Answer:
Positive correlation occurs when larger values of one variable tend to be associated with larger values of the other variable.
Mathematics
Q104.
What is negative correlation?
Answer:
Negative correlation occurs when larger values of one variable tend to be associated with smaller values of the other variable.
Mathematics
Q105.
What is a line of best fit?
Answer:
A line of best fit is a line drawn through a scatter graph to represent the overall trend in the data.
Mathematics
Q106.
What is a cumulative frequency graph used for?
Answer:
A cumulative frequency graph can be used to estimate the median, quartiles, percentiles and interquartile range.
Mathematics
Q107.
What is the interquartile range?
Answer:
The interquartile range is the difference between the upper quartile and lower quartile: IQR = Q3 - Q1.
Mathematics
Q108.
What is a box plot?
Answer:
A box plot displays the minimum, lower quartile, median, upper quartile and maximum of a data set.
Mathematics
Q109.
What is the probability of an event and its complement combined?
Answer:
The probabilities of an event and its complement add to 1.
Mathematics
Q110.
What is the product rule for independent probabilities?
Answer:
For independent events A and B, the probability that both occur is P(A and B) = P(A) × P(B).
Mathematics
Q111.
What is a tree diagram?
Answer:
A tree diagram represents possible outcomes of a sequence of events and can be used to calculate probabilities.
Mathematics
Q112.
What is a bearing?
Answer:
A bearing is an angle measured clockwise from north and is normally written as a three-digit angle.
Mathematics
Q113.
What is an exact value in mathematics?
Answer:
An exact value is a value expressed without rounding, such as π, √2 or 1/3.
Mathematics
Q114.
Why is estimation useful?
Answer:
Estimation provides a quick approximate answer and helps identify whether a calculated result is reasonable.
Mathematics
Q115.
What does the discriminant tell us about a quadratic equation?
Answer:
The discriminant is b² - 4ac. If it is positive there are two distinct real solutions, if it is zero there is one repeated real solution, and if it is negative there are no real solutions.
Mathematics
Q116.
What is a direct proportion?
Answer:
Two quantities are directly proportional when one is a constant multiple of the other. Their ratio remains constant.
Mathematics
Q117.
What is the gradient of the line passing through (2, 5) and (6, 13)?
Answer:
The gradient is (13 - 5) / (6 - 2) = 8 / 4 = 2.
Mathematics
Q118.
What is the relationship between sine, cosine and tangent in a right-angled triangle?
Answer:
For an angle θ, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent.
Mathematics
Q119.
What is compound interest?
Answer:
Compound interest is interest calculated on the original amount and on interest that has already been added. The amount after n periods can be calculated using A = P(1 + r)^n when r is the interest rate per period expressed as a decimal.